(4) Compared to the work in [1]}, we extend the cost functional into a general case, which is similar to the LQ part in [2]}. However, two new adjoint equations are introduced. In fact, we adopt an indirect and hierarchical method to deal with it. In Step 1, we obtain the global maximum principle of optimal control problem for completly observed forward-backward system with random jumps, where it is equivalent to consider the expectation \(E\)  or \(\bar{E}\)  and the cost functional is considered as a special recursive form:
\(J(u)=E[y_0^u].\) 
